If the paper has been refereed and the referee has not suggested adding an appendix, you should not do Option 2 (or at least you need to get a permission from the handling editor/referee). If the paper has not been refereed yet, you can do whatever you and your co-authors want. Option 1 (publishing a 1-page separate paper) is bad.
A review paper summarises the current state of knowledge. Stating opening problems (untapped aspects) adds value and can be included. I see no reason to include such problems in an appendix; they could appear in the main body. It's a personal preference as to whether they appear in your review paper or a separate paper which states the problem and provides a solution. At least, it is without further details. E.g., if the open problem is unknown, worthy of extended discussion, and/or identification has value, then unveiling in a separate paper focusing on the problem/solution may have benefits.